Number of multisets occurring as the peak heights multiset of a Dyck n-path.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =20a(6) =45a(7) =98a(8) =211a(9) =445a(10) =927a(11) =1909a(12) =3901a(13) =7920a(14) =16011a(15) =32260a(16) =64852a(17) =130157a(18) =260932a(19) =522691a(20) =1046489a(21) =2094438a(22) =4190798a(23) =8384100a(24) =16771453a(25) =33547094a(26) =67099568a(27) =134205996a(28) =268420714a(29) =536852452